600 



In Fig. 3, where A and B 

 are the centres of the molecules 

 1 and 2, so that AB = i\, 

 the hatched spherical segment 

 represents the space disposable 

 for molecule 3. The volume of 

 this segment is: 



Multiplication by 12 ni\^d)\ and integration between t -\- o and 

 2t gives for the contribution to S^ : 



n' 



12 



\\lr'- 30r*^- 3t^^- + 20T»rt' + 3tV/^— 6to* 



b. Now not the whole sphe- 

 rical segment CDFE of Fig. 3 

 is at the disposal of molecule 

 3, but only the part of it that 

 % is not overlapped by the sphere 

 of distance of molecule 2 (sphere 

 BG), which part has been 

 represented hatched in fig. 4^). 

 After integration with respect 



{30t%j \ '6rUf -20r''ö*— 39r'<J^4-6Tr>'4-3f)« 



to i\ between t and r -\- <i this gives: 



12 

 2. r>r, >o. 



This part too must again be subdivided, this time into: 



a. T ^ ]\ > 'la. 



b. 2ö > r, > o. 



a. The space disposable for molecule 3 (the hatched part in Fig. 

 5) is now bounded by: sphere AB with i-adius ;\ (as /•, ^ yj, plane 

 CDG (as r, ^ /■,), and sphere BF with radius a (sphere of distance 

 of molecule 2). Conli-ibution to >S\ after integration with respect to 

 r, between 2 o and r -. 



rr/ 



12 



}5t« — 32T'(j= + l«T'ö'-136a''' 



b. Space at the disposal of molecule 3 bounded in the same way 

 as sub a\ now sphere BF cuts, however, the plane CDF, so that 

 only an annular space (hatched) is left. 



i) in drawing this figure the supposition r < 2(7 has been neglected. 



